1. Field of the Invention
This invention relates generally to spectrum analysis and, more particularly, to tone detection by discrete-time filtering.
2. Description of the Prior Art
In many diverse applications, it is necessary to detect the presence of a signal within selected frequency bands and, particularly for a signal comprising a single tone, to estimate the frequency of the tone which may appear randomly in any band. This detection and estimation is generally accomplished in conventional analog systems by utilizing a bank of filters tuned to different, narrowband portions of the spectrum or by employing a single filter which is effectively swept across the bands of interest. Associated with such techniques, however, are the usual problems of analog processors, including unpredictability due to inherent variability of system components.
A discrete-time technique for partitioning the given frequency bands into subbands for detection purposes is described in companion references. The first is a letter by V. Cappellini entitled "Digital Filtering With Sampled Signal Spectrum Frequency Shift", published in the Proceedings of the IEEE, February, 1969, pages 241 and 242. The other reference is an article by V. Cappellini et al entitled "A Special-Purpose On-Line Processor for Bandpass Analysis," appearing in the IEEE Transactions on Audio and Electroacoustics, June, 1970, pages 188-194. In accordance with the technique of the references, the input signal (bandlimited to .omega..sub.m) is sampled at the frequency 2.omega..sub.m so as to alias the portion of the baseband from -.omega..sub.m to 0 into the band .omega..sub.m to 2.omega..sub.m and the sampled signal is processed in two parallel paths. In one path, the sampled signal is filtered with a time-shared, low-pass filter having an initial cutoff frequency of .omega..sub.m /2, thereby developing a signal representation of the input signal's spectrum from 0 to .omega..sub.m /2. In the other path, the sampled signal is shifted in frequency by .omega..sub.m by multiplying the elements of the sampled sequence by (-1).sup.n, and the shifted signal is filtered with the same low-pass filter, thereby developing a signal representation of the input signal's spectrum from .omega..sub.m /2 to .omega..sub.m. In this manner, the digital signals at the output of the two paths are now bandlimited to .omega..sub.m /2. By reducing the sampling rate or decimating by a factor of 2, this approach can be reapplied to each of the two developed signals to obtain four signals, with each output signal now representing a different quarter of the spectrum of the input signal. In this fashion, with an increased number of decimation stages and time-sharing of a single digital filter, successively narrower bands can be evaulated. Thus, the main advantage of this decimation approach for partitioning a given frequency band into several subbands is that a single, fixed low-pass digital filter is required; bandpass analysis can be achieved efficiently with a unique digital filter having fixed coefficients at each stage of decimation.
In a variety of applications, it is known that the spectrum of interest contains, at most, a single spectral line since the input signal is a tone. When this a priori condition is known to exist, the method of Cappellini et al possesses inherent disadvantages. Since general filtering is effected at each decimation stage, numerous multiplications and additions must be performed during the filtering operations of each stage. Another disadvantage is the numerous memory locations required to store samples from the geometrically increasing number of iterated signals.